For Mitt Romney, now begins the hard part. Five decisive primary victories Tuesday confirmed that he will be the Republican Party’s presidential nominee in November. But as Mr. Romney squares off against President Obama, he faces multiple challenges.

Romney is still not well known to general election voters, and polls show he faces a massive deficit on likability against the president. Though he governed solid-blue Massachusetts as a moderate, he has spent the past six years trying to recast himself as a conservative. His party’s base is rallying around him, but not with any marked enthusiasm.

And in perhaps his biggest challenge, Romney is up against an incumbent president who faced no primary challenge and has been actively preparing for the general election for more than a year. Mr. Obama brings to the table all the fundraising, organization, and media attention that naturally flow to a sitting president.

Despite it all, Romney begins the general election season polling close to Obama, who is hobbled by a weak economy. Republicans, fueled by the tea party anger that burst forth three years ago, are eager to unseat him, and even if conservatives aren’t excited about Romney, they are animated by the prospect of defeating Obama. Money will flow both to Romney’s campaign and to the outside groups that are expected to make the campaign especially nasty.

And as a poorly known challenger, Romney has a greater potential upside with voters than the well-known president – particularly with the independent voters who will decide the election.

In his victory speech Tuesday night, Romney set his sights squarely on Obama, accusing him of making “false promises” and offering “weak leadership.” Romney echoed the famous question that then-candidate Ronald Reagan posed in 1980, the last Republican to unseat a Democratic president: Are you better off now than you were four years ago?

“Is it easier to make ends meet? Is it easier to sell your home or buy a new one?” Romney asked, speaking to a crowd in the battleground state of New Hampshire.

“If the answer were yes to those questions, then President Obama would be running for reelection based on his achievements and rightly so,” Romney said. “But because he has failed, he will run a campaign of diversions and distractions and distortions.”

Romney also echoed the winning campaign message of the last Democrat, Bill Clinton, to defeat an incumbent Republican, the first President Bush: “It’s the economy, stupid.”

In Delaware, Newt Gingrich made a push to win, campaigning heavily there and securing the endorsements of key Republicans, including a last-minute switch by the state’s GOP national committeewoman, Priscilla Rakestraw. Romney still won, but with his lowest percentage of the five states, 56.5 percent. Former House Speaker Gingrich came in second with 27 percent.

In a speech Tuesday night in Concord, N.C., Gingrich did not drop out of the race, instead vowing to press on.

“Over the next few days, we are going to look realistically at where we’re at,” Gingrich said, who faces a campaign debt of $4 million. North Carolina holds its primary on May 8.

But going into Tuesday, questions lingered over former Sen. Rick Santorum of Pennsylvania, who dropped out of the race more than two weeks ago, on April 10, amid signs that he might lose his home state’s primary. Romney won the Pennsylvania primary with 58 percent of the vote, and Mr. Santorum came in second with 18 percent.

In an interview Tuesday night with CNN’s Piers Morgan, Santorum came close to endorsing Romney, but not quite.

“He’s the person that is going to go up against Barack Obama it’s pretty clear and we need to win this race. We need to beat Barack Obama,” Santorum said of Romney.

Morgan replied: “You just endorsed Mitt Romney?”

Santorum told Morgan he could “call it whatever you want.” Santorum also said he would be meeting with Romney staff members on Wednesday. There have been reports that Santorum will meet with Romney himself on May 4.

The Pennsylvania primary brought news of a different sort Tuesday night: Two centrist Democratic House members – part of the party’s dwindling Blue Dog coalition – lost their seats to more liberal challengers in the Democratic primary. In one race, pitting two incumbents against each other due to redistricting, Rep. Mark Critz defeated Rep. Jason Altmire. In another race, 10-term Rep. Tim Holden lost in an upset to political newcomer Matt Cartwright.

Both Congressman Altmire and Congressman Holden had voted against Obama’s health-care reform. Their defeats offer yet more evidence of growing partisan polarization in Congress, a challenge for whomever wins the presidency in November.

In the current Congress, the Blue Dog coalition has only 26 members, down from 54 in the previous Congress.